Development of hatching ability in red-eyed treefrogs: escape from complications

Authors: MJ Salazar-Nicholls1,3, KD Escobar2 & KM Warkentin3 1. Pontificia Universidad Católica, Ecuador; 2. Western Connecticut State University; 3. Boston Affiliations: University – – Warkentin Lab

Agalychnis callidryas

Agalychnis callidryas

wasp attacking Agalychnis callidryas clutch

wasp attacking Agalychnis callidryas clutch

Brief Introduction

Hatching early allows embryos to escape threats to eggs, but increases risks to larvae. Red-eyed treefrogs, Agalychnis callidryas, hatch by rapidly releasing enzymes to digest a small hole in their membrane, then squeezing out aided by turgor pressure. Displacement from the initial hole can occur spontaneously and in predator attacks, complicating hatching by capsular collapse as fluid escapes.

Objective

Assess developmental changes in ability to recover from hatching complications

Methods

  • Collected young *A. callidryas clutches from pond, maintained in lab at Smithsonian Tropical Research Institute, Gamboa, Panama
  • Induced individual 3– 5 day old embryos to begin hatching, using hypoxia and mechanosensory stimuli
  • Manually displaced embryo in egg, interrupting exit through initial rupture
  • Recorded macro-video until embryo exited its capsule; rescued individuals that failed to hatch after 30 minutes
  • Analyzed only videos where manipulation was performed successfully
Flooding Jiggling
we submerged younger eggs in hypoxic water (N = 25, 27 at ages 3 and 4 d) we used a blunt probe to move older eggs on clutches (N = 64, 51 at ages 4 and 5 d)

R1: rupture one

R2: rupture two

Outline

This is an analysis of the data used for a poster presentation at SICB 2017, which now is part of a manuscript. The statistical analyses presented in the poster were made using JMP-data analysis sorfware

  1. Load and data cleaning
  2. Mosaic plots, contingency analysis
  3. Wilcoxon test
  4. Box plots
#install.packages("MASS")
#install.packages("coin")

Loading required libraries

library(curl)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
library(plotly)
## 
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
## 
##     last_plot
## The following object is masked from 'package:stats':
## 
##     filter
## The following object is masked from 'package:graphics':
## 
##     layout
library(EnvStats)
## 
## Attaching package: 'EnvStats'
## The following objects are masked from 'package:stats':
## 
##     predict, predict.lm
## The following object is masked from 'package:base':
## 
##     print.default
library(MASS)
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:EnvStats':
## 
##     boxcox
## The following object is masked from 'package:plotly':
## 
##     select
## The following object is masked from 'package:dplyr':
## 
##     select
library(coin)
## Loading required package: survival

Data loading

f <- curl("https://raw.githubusercontent.com/mjsalnic/mjsalnic-data-replication-assignment/master/HC2016R.csv")
HC2016R <- read.csv(f, header = TRUE, sep = ";",dec=",", stringsAsFactors = FALSE)
head(HC2016R)
##   Treatment ClutchN Age Stage comst groupst DecimaClocklHours
## 1  Flooding     462   3     2   2-3     2-3             20.23
## 2  Flooding     470   3     3   2-3     2-3             21.02
## 3  Flooding     386   4     4   4-5     4-7              0.15
## 4  Flooding     397   4     5   4-5     4-7              0.82
## 5  Flooding     102   4     5   4-5     4-7             10.85
## 6  Flooding     187   4     4   4-5     4-7             16.12
##   AccumshakingtimeRup1Fra AccumShakingR1sec NumPosChanADBefore2ndHole
## 1                       4              0.13                         3
## 2                     290              9.67                         7
## 3                      30              1.00                         1
## 4                     395             13.17                         1
## 5                     105              3.50                        17
## 6                     260              8.67                         1
##   AccumADshakingR AccumshakingtimeRup2Fra AccumShakingR2sec DisEndRup2Fr
## 1              NA                      NA                NA           NA
## 2              NA                       0                 0           NA
## 3              NA                       0                 0           NA
## 4              NA                      NA                NA           NA
## 5              NA                       0                 0           NA
## 6              NA                      NA                NA           NA
##   DisEndHatchingStartFr CompDurFr CompressionSec CompressionSeen
## 1                  1407        NA             NA               0
## 2                  4838        NA             NA               0
## 3                   916         6           0.20               1
## 4                  5182        NA             NA               0
## 5                  6511         7           0.23               1
## 6                  2222        NA             NA               0
##   EXITDURATIONFr EXIT.DURATION.StarttoFullyOutsec NumHoles
## 1           2442                       81.4000000        1
## 2           1318                       43.9333333        1
## 3            342                       11.4000000        1
## 4              4                        0.1333333        1
## 5           3995                      133.1666667        1
## 6            157                        5.2333333        1
##   FirstSecondHoleExit Rescue X X.1
## 1               First      0      
## 2               First      0      
## 3               First      0      
## 4               First      0      
## 5               First      0      
## 6               First      0
attach(HC2016R)

Transforming numerical variables to factorial ### Exit duration

HC2016R$Stage<- factor(HC2016R$Stage)
HC2016R$Age<- factor(HC2016R$Age)
HC2016R$NumHoles<- factor(HC2016R$NumHoles)
HC2016R$Rescue<- factor(HC2016R$Rescue)

str(HC2016R)
## 'data.frame':    167 obs. of  25 variables:
##  $ Treatment                       : chr  "Flooding" "Flooding" "Flooding" "Flooding" ...
##  $ ClutchN                         : int  462 470 386 397 102 187 272 268 239 244 ...
##  $ Age                             : Factor w/ 3 levels "3","4","5": 1 1 2 2 2 2 2 2 2 2 ...
##  $ Stage                           : Factor w/ 6 levels "2","3","4","5",..: 1 2 3 4 4 3 4 3 5 5 ...
##  $ comst                           : chr  "2-3" "2-3" "4-5" "4-5" ...
##  $ groupst                         : chr  "2-3" "2-3" "4-7" "4-7" ...
##  $ DecimaClocklHours               : num  20.23 21.02 0.15 0.82 10.85 ...
##  $ AccumshakingtimeRup1Fra         : int  4 290 30 395 105 260 285 0 307 170 ...
##  $ AccumShakingR1sec               : num  0.13 9.67 1 13.17 3.5 ...
##  $ NumPosChanADBefore2ndHole       : int  3 7 1 1 17 1 1 14 16 1 ...
##  $ AccumADshakingR                 : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ AccumshakingtimeRup2Fra         : int  NA 0 0 NA 0 NA NA NA 385 NA ...
##  $ AccumShakingR2sec               : num  NA 0 0 NA 0 ...
##  $ DisEndRup2Fr                    : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ DisEndHatchingStartFr           : int  1407 4838 916 5182 6511 2222 213 8227 5455 187 ...
##  $ CompDurFr                       : int  NA NA 6 NA 7 NA NA NA NA NA ...
##  $ CompressionSec                  : num  NA NA 0.2 NA 0.23 NA NA NA NA NA ...
##  $ CompressionSeen                 : int  0 0 1 0 1 0 0 0 0 0 ...
##  $ EXITDURATIONFr                  : int  2442 1318 342 4 3995 157 96 NA NA 147 ...
##  $ EXIT.DURATION.StarttoFullyOutsec: num  81.4 43.933 11.4 0.133 133.167 ...
##  $ NumHoles                        : Factor w/ 2 levels "1","2": 1 1 1 1 1 1 1 1 2 1 ...
##  $ FirstSecondHoleExit             : chr  "First" "First" "First" "First" ...
##  $ Rescue                          : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
##  $ X                               : chr  "" "" "" "" ...
##  $ X.1                             : chr  "" "" "" "" ...

let’s subset the data into 2 outcome groups: success_hat (hatched embryos after displacement) and failed_hat(embryos unable to hatch after displacement)

success_hat<-subset(HC2016R, Rescue==0, na.rm=T)
failed_hat<-subset(HC2016R, Rescue==1, na.rm=T)

let’s subset the data into 2 treatment groups: flooding and jiggling

flooding<-subset (HC2016R, Treatment=="Flooding", na.rm=T)
jiggling<-subset(HC2016R, Treatment=="Jiggling", na.rm=T)

Explore if there are differences in the outcome between treatments ## Results

Escape-hatching success after complications

There are not differences between treatments

  1. Mosaic plot - graphical representation of the frequency of successul hatching and unable to hatch after displacement experiment (combined experiments)
totals=table(HC2016R$Stage,HC2016R$Rescue)
mosaicplot(totals, main = "Escape-hatching success after complications", xlab = "Embryonic developmental stage", ylab = "proportion of embryos", col=c("light green", "black"))

#where 0 means no rescue needed, embryo able to hatch by itself and 1 means rescue after displacement experiment

1= Failed to hatch 0= Succesfully hatched embryos

Stage: P < 0.0001

  1. Contingency table- Escape-hatching success after complications
tab1<-table(HC2016R$Stage, HC2016R$Rescue)
prop.table(tab1)*100
##    
##             0         1
##   2  2.395210  4.191617
##   3  5.988024  1.796407
##   4 11.377246  0.000000
##   5 20.359281  1.796407
##   6 20.958084  0.000000
##   7 31.137725  0.000000
chisq.test(tab1)
## Warning in chisq.test(tab1): Chi-squared approximation may be incorrect
## 
##  Pearson's Chi-squared test
## 
## data:  tab1
## X-squared = 60.99, df = 5, p-value = 7.588e-12
fisher.test(tab1)
## 
##  Fisher's Exact Test for Count Data
## 
## data:  tab1
## p-value = 9.464e-09
## alternative hypothesis: two.sided

Multiple membrane ruptures

  1. Treatments together
tab<-table(HC2016R$Stage, HC2016R$NumHoles)
prop.table(tab)*100
##    
##             1         2
##   2  4.790419  1.796407
##   3  1.796407  5.988024
##   4  2.395210  8.982036
##   5  7.185629 14.970060
##   6  8.982036 11.976048
##   7  7.784431 23.353293
chisq.test(tab)
## Warning in chisq.test(tab): Chi-squared approximation may be incorrect
## 
##  Pearson's Chi-squared test
## 
## data:  tab
## X-squared = 12.719, df = 5, p-value = 0.02616
fisher.test(tab)
## 
##  Fisher's Exact Test for Count Data
## 
## data:  tab
## p-value = 0.03435
## alternative hypothesis: two.sided
  1. Mosaic plot- multiple membrane ruptures - Flooding treatment
attach(flooding)
## The following objects are masked from HC2016R:
## 
##     AccumADshakingR, AccumShakingR1sec, AccumShakingR2sec,
##     AccumshakingtimeRup1Fra, AccumshakingtimeRup2Fra, Age,
##     ClutchN, CompDurFr, CompressionSec, CompressionSeen, comst,
##     DecimaClocklHours, DisEndHatchingStartFr, DisEndRup2Fr,
##     EXIT.DURATION.StarttoFullyOutsec, EXITDURATIONFr,
##     FirstSecondHoleExit, groupst, NumHoles,
##     NumPosChanADBefore2ndHole, Rescue, Stage, Treatment, X, X.1
totals=table(flooding$Stage,flooding$NumHoles)
mosaicplot(totals, main = "Multiple membrane ruptures", xlab = "Embryonic developmental stage", ylab = "Proportion of embryos", col=c("light green", "black"))

p-value = 0.009272

2.1 Contigency table- Multiple membrane ruptures

tab2<-table(flooding$Stage, flooding$NumHoles)
fisher.test(tab2)
## 
##  Fisher's Exact Test for Count Data
## 
## data:  tab2
## p-value = 0.009272
## alternative hypothesis: two.sided
  1. Mosaic plot- multiple membrane ruptures - Jiggling treatment
totals=table(jiggling$Stage,jiggling$NumHoles)
mosaicplot(totals, main = "Multiple membrane ruptures", xlab = "Embryonic developmental stage", ylab = "Proportion of embryos", col=c("light green", "black"))

p-value = 0.1508

3.1 Contigency table- Multiple membrane ruptures

tab3<-table(jiggling$Stage, jiggling$NumHoles)
fisher.test(tab3)
## 
##  Fisher's Exact Test for Count Data
## 
## data:  tab3
## p-value = 0.1508
## alternative hypothesis: two.sided
summary(tab3)
## Number of cases in table: 115 
## Number of factors: 2 
## Test for independence of all factors:
##  Chisq = NaN, df = 5, p-value = NA
##  Chi-squared approximation may be incorrect

Position changes after displacement – search for initial rupture site

Should we use parametric or non-parametric test?

par(mfrow=c(3,2))
hist(HC2016R$NumPosChanADBefore2ndHole[HC2016R$Stage=="2"])
hist(HC2016R$NumPosChanADBefore2ndHole[HC2016R$Stage=="3"])
hist(HC2016R$NumPosChanADBefore2ndHole[HC2016R$Stage=="4"])
hist(HC2016R$NumPosChanADBefore2ndHole[HC2016R$Stage=="5"])
hist(HC2016R$NumPosChanADBefore2ndHole[HC2016R$Stage=="6"])
hist(HC2016R$NumPosChanADBefore2ndHole[HC2016R$Stage=="7"])

par(mfrow=c(1,2))
boxplot(NumPosChanADBefore2ndHole~Stage,success_hat)

boxplot(NumPosChanADBefore2ndHole~Stage,failed_hat)

Subsetting data frame: to extract only values from the earliest stages where embryos got more trouble making a second hole to hatch

young_outcome<- subset(HC2016R, comst="2-3", select = NumPosChanADBefore2ndHole:Rescue)

str(young_outcome)
## 'data.frame':    167 obs. of  14 variables:
##  $ NumPosChanADBefore2ndHole       : int  3 7 1 1 17 1 1 14 16 1 ...
##  $ AccumADshakingR                 : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ AccumshakingtimeRup2Fra         : int  NA 0 0 NA 0 NA NA NA 385 NA ...
##  $ AccumShakingR2sec               : num  NA 0 0 NA 0 ...
##  $ DisEndRup2Fr                    : int  NA NA NA NA NA NA NA NA NA NA ...
##  $ DisEndHatchingStartFr           : int  1407 4838 916 5182 6511 2222 213 8227 5455 187 ...
##  $ CompDurFr                       : int  NA NA 6 NA 7 NA NA NA NA NA ...
##  $ CompressionSec                  : num  NA NA 0.2 NA 0.23 NA NA NA NA NA ...
##  $ CompressionSeen                 : int  0 0 1 0 1 0 0 0 0 0 ...
##  $ EXITDURATIONFr                  : int  2442 1318 342 4 3995 157 96 NA NA 147 ...
##  $ EXIT.DURATION.StarttoFullyOutsec: num  81.4 43.933 11.4 0.133 133.167 ...
##  $ NumHoles                        : Factor w/ 2 levels "1","2": 1 1 1 1 1 1 1 1 2 1 ...
##  $ FirstSecondHoleExit             : chr  "First" "First" "First" "First" ...
##  $ Rescue                          : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
par(mfrow=c(1,2))
hist(young_outcome$NumPosChanADBefore2ndHole[young_outcome$Rescue=="1"])
hist(young_outcome$NumPosChanADBefore2ndHole[young_outcome$Rescue=="0"])

boxplot(data = young_outcome, NumPosChanADBefore2ndHole ~ Rescue, col = c("burlywood2", 
    "lightpink1"))

wilcox.test(NumPosChanADBefore2ndHole~Rescue, data = young_outcome, correct=FALSE)
## 
##  Wilcoxon rank sum test
## 
## data:  NumPosChanADBefore2ndHole by Rescue
## W = 160, p-value = 8.265e-08
## alternative hypothesis: true location shift is not equal to 0

p-value = < 0.0001 N= 10,14

boxplot(data = success_hat, NumPosChanADBefore2ndHole ~ comst, col = c("burlywood2", 
    "lightpink1", "purple"))

kruskal.test(NumPosChanADBefore2ndHole ~ comst,
             data =success_hat)
## 
##  Kruskal-Wallis rank sum test
## 
## data:  NumPosChanADBefore2ndHole by comst
## Kruskal-Wallis chi-squared = 2.7825, df = 2, p-value = 0.2488

p-value = 0.2488 N = 14, 53, 84

Exit from egg: fist or second rupture

boxplot(data = success_hat, NumPosChanADBefore2ndHole ~ NumHoles, col = c("burlywood2", 
    "lightpink1"))

wilcox.test(NumPosChanADBefore2ndHole~NumHoles, data = success_hat, correct=FALSE)
## 
##  Wilcoxon rank sum test
## 
## data:  NumPosChanADBefore2ndHole by NumHoles
## W = 3450.5, p-value = 3.33e-06
## alternative hypothesis: true location shift is not equal to 0

P < 0.0001 N = 41, 110

Exit duration

#good one
attach(success_hat)
## The following objects are masked from flooding:
## 
##     AccumADshakingR, AccumShakingR1sec, AccumShakingR2sec,
##     AccumshakingtimeRup1Fra, AccumshakingtimeRup2Fra, Age,
##     ClutchN, CompDurFr, CompressionSec, CompressionSeen, comst,
##     DecimaClocklHours, DisEndHatchingStartFr, DisEndRup2Fr,
##     EXIT.DURATION.StarttoFullyOutsec, EXITDURATIONFr,
##     FirstSecondHoleExit, groupst, NumHoles,
##     NumPosChanADBefore2ndHole, Rescue, Stage, Treatment, X, X.1
## The following objects are masked from HC2016R:
## 
##     AccumADshakingR, AccumShakingR1sec, AccumShakingR2sec,
##     AccumshakingtimeRup1Fra, AccumshakingtimeRup2Fra, Age,
##     ClutchN, CompDurFr, CompressionSec, CompressionSeen, comst,
##     DecimaClocklHours, DisEndHatchingStartFr, DisEndRup2Fr,
##     EXIT.DURATION.StarttoFullyOutsec, EXITDURATIONFr,
##     FirstSecondHoleExit, groupst, NumHoles,
##     NumPosChanADBefore2ndHole, Rescue, Stage, Treatment, X, X.1
#good one
p <- ggplot(data=success_hat, aes(x=Stage, y=EXIT.DURATION.StarttoFullyOutsec, fill=Stage))+stat_boxplot(geom='errorbar', linetype=1, width=0.5)+  #whiskers
geom_boxplot(outlier.shape=1)
p <- p + geom_boxplot()+ stat_summary(fun.y = mean, geom = "point", shape=5, size=5, fill="white")
p <- p + theme(axis.text.x=element_text(angle=0))
p <- p + ylab("Exit duration (sec)")
p <- p + stat_n_text(y.pos = 170)
p <- p + theme_classic()+ scale_fill_manual(breaks = c("2", "3", "4", "5", "6", "7"), 
                       values=c("lightskyblue", "lightskyblue", "mediumaquamarine","mediumturquoise" ,"mediumturquoise","olivedrab2"))
p
## Warning: Removed 42 rows containing non-finite values (stat_boxplot).

## Warning: Removed 42 rows containing non-finite values (stat_boxplot).

## Warning: Removed 42 rows containing non-finite values (stat_boxplot).
## Warning: Removed 42 rows containing non-finite values (stat_summary).
## Warning: Removed 42 rows containing non-finite values (stat_n_text).

Body Compression

totals1=table(success_hat$comst,success_hat$CompressionSeen)
mosaicplot(totals1, main = "Escape-hatching success after complications", xlab = "Embryonic developmental stage", ylab = "proportion of embryos", col=c("light green", "pink"))

p <- ggplot(data=success_hat, aes(x=groupst, y= CompressionSec, fill=groupst))+stat_boxplot(geom='errorbar', linetype=1, width=0.5)+  #whiskers
geom_boxplot(outlier.shape=1)
p <- p + geom_boxplot()+ stat_summary(fun.y = mean, geom = "point", shape=5, size=5, fill="white")
p <- p + theme(axis.text.x=element_text(angle=0))
p <- p + ylab("Compression Duration (sec)") + xlab("Developmental stage")
p <- p + stat_n_text(y.pos = 70)
p <- p + theme_classic()+ scale_fill_manual(breaks = c("2,3", "4,7"), 
                       values=c("lightskyblue", "mediumaquamarine"))
p
## Warning: Removed 124 rows containing non-finite values (stat_boxplot).

## Warning: Removed 124 rows containing non-finite values (stat_boxplot).

## Warning: Removed 124 rows containing non-finite values (stat_boxplot).
## Warning: Removed 124 rows containing non-finite values (stat_summary).
## Warning: Removed 124 rows containing non-finite values (stat_n_text).

detach(flooding)
attach(success_hat)
## The following objects are masked from success_hat (pos = 3):
## 
##     AccumADshakingR, AccumShakingR1sec, AccumShakingR2sec,
##     AccumshakingtimeRup1Fra, AccumshakingtimeRup2Fra, Age,
##     ClutchN, CompDurFr, CompressionSec, CompressionSeen, comst,
##     DecimaClocklHours, DisEndHatchingStartFr, DisEndRup2Fr,
##     EXIT.DURATION.StarttoFullyOutsec, EXITDURATIONFr,
##     FirstSecondHoleExit, groupst, NumHoles,
##     NumPosChanADBefore2ndHole, Rescue, Stage, Treatment, X, X.1
## The following objects are masked from HC2016R:
## 
##     AccumADshakingR, AccumShakingR1sec, AccumShakingR2sec,
##     AccumshakingtimeRup1Fra, AccumshakingtimeRup2Fra, Age,
##     ClutchN, CompDurFr, CompressionSec, CompressionSeen, comst,
##     DecimaClocklHours, DisEndHatchingStartFr, DisEndRup2Fr,
##     EXIT.DURATION.StarttoFullyOutsec, EXITDURATIONFr,
##     FirstSecondHoleExit, groupst, NumHoles,
##     NumPosChanADBefore2ndHole, Rescue, Stage, Treatment, X, X.1
x <- c(Stage)

x<- factor(x)
levels(x)<- list("St2-3"=c("2","3"), "st 4-7"=c("4", "5", "6", "7"))
x
##   [1] <NA>   St2-3  St2-3  st 4-7 st 4-7 St2-3  st 4-7 St2-3  st 4-7 st 4-7
##  [11] st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7
##  [21] st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 St2-3 
##  [31] st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7
##  [41] st 4-7 st 4-7 st 4-7 st 4-7 <NA>   St2-3  St2-3  St2-3  <NA>   <NA>  
##  [51] St2-3  St2-3  St2-3  St2-3  St2-3  St2-3  st 4-7 st 4-7 St2-3  St2-3 
##  [61] St2-3  St2-3  St2-3  St2-3  St2-3  St2-3  St2-3  St2-3  St2-3  St2-3 
##  [71] st 4-7 St2-3  st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 St2-3 
##  [81] st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 St2-3  st 4-7 st 4-7 st 4-7
##  [91] st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7
## [101] st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7
## [111] st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7
## [121] st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7
## [131] st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7
## [141] st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7 st 4-7
## [151] st 4-7 st 4-7 st 4-7 st 4-7
## Levels: St2-3 st 4-7
boxplot(CompressionSec ~ x, data=success_hat)

p-value = 0.02087

wilcox.test(CompressionSec ~groupst, data=success_hat)
## Warning in wilcox.test.default(x = c(53.27, 7.5, 19.4, 15.4, 9.53, 0.03, :
## cannot compute exact p-value with ties
## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  CompressionSec by groupst
## W = 128, p-value = 0.02087
## alternative hypothesis: true location shift is not equal to 0

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